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Applications · Chemistry, Physics, and Earth Sciences

Sanjeev Raja, Martin Šípka, Michael Psenka, Tobias Kreiman, Michal Pavelka, Aditi Krishnapriyan

Transition path sampling (TPS), which involves finding probable paths connecting two points on an energy landscape, remains a challenge due to the complexity of real-world atomistic systems. Current machine learning approaches rely on expensive training procedures and under-utilize growing quantities of atomistic data, limiting scalability and generalization. Generative models of atomistic conformational ensembles sample temporally independent states from energy landscapes, but their application to TPS remains mostly unexplored. In this work, we address TPS by interpreting candidate paths as trajectories sampled from stochastic dynamics induced by the learned score function of generative models, namely denoising diffusion and flow matching. Under these dynamics, finding high-likelihood transition paths becomes equivalent to minimizing the Onsager-Machlup (OM) action functional, enabling us to repurpose pre-trained generative models for TPS in a zero-shot fashion. We demonstrate our approach on a Müller-Brown potential and several fast-folding proteins, where we obtain diverse, physically realistic transition pathways, as well as tetrapeptides, where we demonstrate successful TPS on systems not seen by the generative model during training. Our method can be easily incorporated into new generative models, making it practically relevant as models continue to scale and improve.

Applications · Chemistry, Physics, and Earth Sciences

Xiang Fu, Brandon Wood, Luis Barroso-Luque, Daniel S. Levine, Meng Gao, Misko Dzamba, Larry Zitnick

Machine learning interatomic potentials (MLIPs) have become increasingly effective at approximating quantum mechanical calculations at a fraction of the computational cost. However, lower errors on held out test sets do not always translate to improved results on downstream physical property prediction tasks. In this paper, we propose testing MLIPs on their practical ability to conserve energy during molecular dynamic simulations. If passed, improved correlations are found between test errors and their performance on physical property prediction tasks. We identify choices which may lead to models failing this test, and use these observations to improve upon highly-expressive models. The resulting model, eSEN, provides state-of-the-art results on a range of physical property prediction tasks, including materials stability prediction, thermal conductivity prediction, and phonon calculations.

Applications · Chemistry, Physics, and Earth Sciences

Qingpo Wuwu, Chonghan Gao, Tianyu Chen, Yihang Huang, Yuekai Zhang, Jianing Wang, Jianxin Li, Haoyi Zhou, Shanghang Zhang

Solving partial differential equations (PDEs) using neural methods has been a long-standing scientific and engineering research pursuit. Physics-Informed Neural Networks (PINNs) have emerged as a promising alternative to traditional numerical methods for solving PDEs. However, the gap between domain-specific knowledge and deep learning expertise often limits the practical application of PINNs. Previous works typically involve manually conducting extensive PINNs experiments and summarizing heuristic rules for hyperparameter tuning. In this work, we introduce PINNsAgent, a novel surrogation framework that leverages large language models (LLMs) to bridge the gap between domain-specific knowledge and deep learning. PINNsAgent integrates Physics-Guided Knowledge Replay (PGKR) for efficient knowledge transfer from solved PDEs to similar problems, and Memory Tree Reasoning for exploring the search space of optimal PINNs architectures. We evaluate PINNsAgent on 14 benchmark PDEs, demonstrating its effectiveness in automating the surrogation process and significantly improving the accuracy of PINNs-based solutions.

Applications · Chemistry, Physics, and Earth Sciences

Yi He, Yiming Yang, Xiaoyuan Cheng, Hai Wang, Xiao Xue, Boli Chen, Yukun Hu

Generating long-term trajectories of dissipative chaotic systems autoregressively is a highly challenging task. The inherent positive Lyapunov exponents amplify prediction errors over time.Many chaotic systems possess a crucial property — ergodicity on their attractors, which makes long-term prediction possible. State-of-the-art methods address ergodicity by preserving statistical properties using optimal transport techniques. However, these methods face scalability challenges due to the curse of dimensionality when matching distributions. To overcome this bottleneck, we propose a scalable transformer-based framework capable of stably generating long-term high-dimensional and high-resolution chaotic dynamics while preserving ergodicity. Our method is grounded in a physical perspective, revisiting the Von Neumann mean ergodic theorem to ensure the preservation of long-term statistics in the $\mathcal{L}^2$ space. We introduce novel modifications to the attention mechanism, making the transformer architecture well-suited for learning large-scale chaotic systems. Compared to operator-based and transformer-based methods, our model achieves better performances across five metrics, from short-term prediction accuracy to long-term statistics. In addition to our methodological contributions, we introduce new chaotic system benchmarks: a machine learning dataset of 140$k$ snapshots of turbulent channel flow and a processed high-dimensional Kolmogorov Flow dataset, along with various evaluation metrics for both short- and long-term performances. Both are well-suited for machine learning research on chaotic systems.

Applications · Chemistry, Physics, and Earth Sciences

Ziyang Yu, Wenbing Huang, Yang Liu

Molecular Dynamics (MD) simulations are essential for understanding the atomic-level behavior of molecular systems, giving insights into their transitions and interactions. However, classical MD techniques are limited by the trade-off between accuracy and efficiency, while recent deep learning-based improvements have mostly focused on single-domain molecules, lacking transferability to unfamiliar molecular systems. Therefore, we propose **Uni**fied **Sim**ulator (UniSim), which leverages cross-domain knowledge to enhance the understanding of atomic interactions. First, we employ a multi-head pretraining approach to learn a unified atomic representation model from a large and diverse set of molecular data. Then, based on the stochastic interpolant framework, we learn the state transition patterns over long timesteps from MD trajectories, and introduce a force guidance module for rapidly adapting to different chemical environments. Our experiments demonstrate that UniSim achieves highly competitive performance across small molecules, peptides, and proteins.

Applications · Chemistry, Physics, and Earth Sciences

Jiahua Rao, Dahao Xu, Wentao Wei, Yicong Chen, Mingjun Yang, Yuedong Yang

While Graph Neural Networks and Transformers have shown promise in predicting molecular properties, they struggle with directly modeling complex many-body interactions. Current methods often approximate interactions like three- and four-body terms in message passing, while attention-based models, despite enabling direct atom communication, are typically limited to triplets, making higher-order interactions computationally demanding. To address the limitations, we introduce MABNet, a geometric attention framework designed to model four-body interactions by facilitating direct communication among atomic quartets. This approach bypasses the computational bottlenecks associated with traditional triplet-based attention mechanisms, allowing for the efficient handling of higher-order interactions. MABNet achieves state-of-the-art performance on benchmarks like MD22 and SPICE. These improvements underscore its capability to accurately capture intricate many-body interactions in large molecules. By unifying rigorous many-body physics with computational efficiency, MABNet advances molecular simulations for applications in drug design and materials discovery, while its extensible framework paves the way for modeling higher-order quantum effects.

Applications · Chemistry, Physics, and Earth Sciences

Muhammed Göktepe, Amir Hossein Shamseddin, Erencan Uysal, Javier Monteagudo, Lukas Drees, Aysim Toker, Senthold Asseng, Malte von Bloh

Satellite imagery is essential for Earth observation, enabling applications like crop yield prediction, environmental monitoring, and climatechange assessment. However, integrating satellite imagery with climate data remains a challenge, limiting its utility for forecasting and scenario analysis. We introduce a novel dataset of 2.9 million Sentinel-2 images spanning 15 land cover types with corresponding climate records, forming the foundation for two satellite image generation approaches using fine-tuned Stable Diffusion 3 models. The first is a text-to-image generation model that uses textual prompts with climate and land cover details to produce realistic synthetic imagery for specific regions. The second leverages ControlNet for multi-conditional image generation, preserving spatial structures while mapping climate data or generating time-series to simulate landscape evolution. By combining synthetic image generation with climate and land cover data, our work advances generative modeling in remote sensing, offering realistic inputs for environmental forecasting and new possibilities for climate adaptation and geospatial analysis.

Applications · Chemistry, Physics, and Earth Sciences

Vignesh Gopakumar, Ander Gray, Lorenzo Zanisi, Timothy Nunn, Daniel Giles, Matt Kusner, Stanislas Pamela, Marc Deisenroth

Simulating complex physical systems is crucial for understanding and predicting phenomena across diverse fields, such as fluid dynamics and heat transfer, as well as plasma physics and structural mechanics. Traditional approaches rely on solving partial differential equations (PDEs) using numerical methods, which are computationally expensive and often prohibitively slow for real-time applications or large-scale simulations. Neural PDEs have emerged as efficient alternatives to these costly numerical solvers, offering significant computational speed-ups. However, their lack of robust uncertainty quantification (UQ) limits deployment in critical applications. We introduce a model-agnostic, physics-informed conformal prediction (CP) framework that provides guaranteed uncertainty estimates without requiring labelled data. By utilising a physics-based approach, we can quantify and calibrate the model's inconsistencies with the physics rather than the uncertainty arising from the data. Our approach utilises convolutional layers as finite-difference stencils and leverages physics residual errors as nonconformity scores, enabling data-free UQ with marginal and joint coverage guarantees across prediction domains for a range of complex PDEs. We further validate the efficacy of our method on neural PDE models for plasma modelling and shot design in fusion reactors.

Applications · Chemistry, Physics, and Earth Sciences

Keyue Qiu, Yuxuan Song, Zhehuan Fan, Peidong Liu, Zhe Zhang, Mingyue Zheng, Hao Zhou, Wei-Ying Ma

Structure-Based Drug Design (SBDD) is crucial for identifying bioactive molecules. Recent deep generative models are faced with challenges in geometric structure modeling. A major bottleneck lies in the twisted probability path of multi-modalities—continuous 3D positions and discrete 2D topologies—which jointly determine molecular geometries. By establishing the fact that noise schedules decide the Variational Lower Bound (VLB) for the twisted probability path, we propose VLB-Optimal Scheduling (VOS) strategy in this under-explored area, which optimizes VLB as a path integral for SBDD. Our model effectively enhances molecular geometries and interaction modeling, achieving state-of-the-art PoseBusters passing rate of 95.9\% on CrossDock, more than 10\% improvement upon strong baselines, while maintaining high affinities and robust intramolecular validity evaluated on held-out test set. Code is available at https://github.com/AlgoMole/MolCRAFT.

Applications · Chemistry, Physics, and Earth Sciences

Yiming Yang, Xiaoyuan Cheng, Daniel Giles, Sibo Cheng, Yi He, Xiao Xue, Boli Chen, Yukun Hu

Variational data assimilation estimates the dynamical system states by minimizing a cost function that fits the numerical models with the observational data. Although four-dimensional variational assimilation (4D-Var) is widely used, it faces high computational costs in complex nonlinear systems and depends on imperfect state-observation mappings. Deep learning (DL) offers more expressive approximators, while integrating DL models into 4D-Var is challenging due to their nonlinearities and lack of theoretical guarantees in assimilation results. In this paper, we propose \textit{Tensor-Var}, a novel framework that integrates kernel conditional mean embedding (CME) with 4D-Var to linearize nonlinear dynamics, achieving convex optimization in a learned feature space. Moreover, our method provides a new perspective for solving 4D-Var in a linear way, offering theoretical guarantees of consistent assimilation results between the original and feature spaces. To handle large-scale problems, we propose a method to learn deep features (DFs) using neural networks within the Tensor-Var framework. Experiments on chaotic systems and global weather prediction with real-time observations show that Tensor-Var outperforms conventional and DL hybrid 4D-Var baselines in accuracy while achieving a 10- to 20-fold speed improvement.

Applications · Chemistry, Physics, and Earth Sciences

Anas Jnini, Lorenzo Breschi, Flavio Vella

Divergence-free symmetric tensors (DFSTs) are fundamental in continuum mechanics, encoding conservation laws such as mass and momentum conservation. We introduce Riemann Tensor Neural Networks (RTNNs), a novel neural architecture that inherently satisfies the DFST condition to machine precision, providing a strong inductive bias for enforcing these conservation laws. We prove that RTNNs can approximate any sufficiently smooth DFST with arbitrary precision and demonstrate their effectiveness as surrogates for conservative PDEs, achieving improved accuracy across benchmarks. This work is the first to use DFSTs as an inductive bias in neural PDE surrogates and to explicitly enforce the conservation of both mass and momentum within a physics-constrained neural architecture.

Applications · Chemistry, Physics, and Earth Sciences

Peter Eckmann, Dongxia Wu, Germano Heinzelmann, Michael Gilson, Rose Yu

Current generative models for drug discovery primarily use molecular docking as an oracle to guide the generation of active compounds. However, such models are often not useful in practice because even compounds with high docking scores do not consistently show real-world experimental activity. More accurate methods for activity prediction exist, such as molecular dynamics based binding free energy calculations, but they are too computationally expensive to use in a generative model. To address this challenge, we propose Multi-Fidelity Latent space Active Learning (MF-LAL), a generative modeling framework that integrates a set of oracles with varying cost-accuracy tradeoffs. Using active learning, we train a surrogate model for each oracle and use these surrogates to guide generation of compounds with high predicted activity. Unlike previous approaches that separately learn the surrogate model and generative model, MF-LAL combines the generative and multi-fidelity surrogate models into a single framework, allowing for more accurate activity prediction and higher quality samples. Our experiments on two disease-relevant proteins show that MF-LAL produces compounds with significantly better binding free energy scores than other single and multi-fidelity approaches (~50% improvement in mean binding free energy score). The code is available at https://github.com/Rose-STL-Lab/MF-LAL.

Applications · Chemistry, Physics, and Earth Sciences

Makoto Takamoto, Viktor Zaverkin, Mathias Niepert

Machine learning is playing an increasingly important role in computational chemistry and materials science, complementing expensive ab initio and first-principles methods. However, machine-learned interatomic potentials (MLIPs) often struggle with generalization and robustness, leading to unphysical energy and force predictions in atomistic simulations. To address this, we propose a physics-informed, weakly supervised training framework for MLIPs. Our method introduces two novel loss functions: one based on Taylor expansions of the potential energy and another enforcing conservative force constraints. This approach enhances accuracy, particularly in low-data regimes, and reduces the reliance on large, expensive training datasets. Extensive experiments across benchmark datasets show up to 2× reductions in energy and force errors for multiple baseline models. Additionally, our method improves the stability of molecular dynamics simulations and facilitates effective fine-tuning of ML foundation models on sparse, high-accuracy ab initio data. An implementation of our method and scripts for executing experiments are available at \url{https://github.com/nec-research/PICPS-ML4Sci}.

Applications · Chemistry, Physics, and Earth Sciences

Koen Minartz, Tim d'Hondt, Leon Hillmann, Jörn Starruß, Lutz Brusch, Vlado Menkovski

The cellular Potts model (CPM) is a powerful computational method for simulating collective spatiotemporal dynamics of biological cells.To drive the dynamics, CPMs rely on physics-inspired Hamiltonians. However, as first principles remain elusive in biology, these Hamiltonians only approximate the full complexity of real multicellular systems.To address this limitation, we propose NeuralCPM, a more expressive cellular Potts model that can be trained directly on observational data.At the core of NeuralCPM lies the Neural Hamiltonian, a neural network architecture that respects universal symmetries in collective cellular dynamics.Moreover, this approach enables seamless integration of domain knowledge by combining known biological mechanisms and the expressive Neural Hamiltonian into a hybrid model.Our evaluation with synthetic and real-world multicellular systems demonstrates that NeuralCPM is able to model cellular dynamics that cannot be accounted for by traditional analytical Hamiltonians.

Applications · Chemistry, Physics, and Earth Sciences

Dong-Hee Shin, Young-Han Son, Hyun Jung Lee, Deok-Joong Lee, Tae-Eui Kam

Molecular discovery has attracted significant attention in scientific fields for its ability to generate novel molecules with desirable properties. Although numerous methods have been developed to tackle this problem, most rely on an online setting that requires repeated online evaluation of candidate molecules using the oracle. However, in real-world molecular discovery, the oracle is often represented by wet-lab experiments, making this online setting impractical due to the significant time and resource demands. To fill this gap, we propose the Molecular Stitching (MolStitch) framework, which utilizes a fixed offline dataset to explore and optimize molecules without the need for repeated oracle evaluations. Specifically, MolStitch leverages existing molecules from the offline dataset to generate novel `stitched molecules' that combine their desirable properties. These stitched molecules are then used as training samples to fine-tune the generative model using preference optimization techniques. Experimental results on various offline multi-objective molecular optimization problems validate the effectiveness of MolStitch. The source code is available online.

Applications · Chemistry, Physics, and Earth Sciences

Ye Liu, Yuntian Chen

Automotive drag coefficient ($C_d$) is pivotal to energy efficiency, fuel consumption, and aerodynamic performance. However, costly computational fluid dynamics (CFD) simulations and wind tunnel tests struggle to meet the rapid-iteration demands of automotive design. We present DragSolver, a Transformer-based framework for rapid and accurate $C_d$ estimation from large-scale, diverse 3D vehicle models.DragSolver tackles four key real-world challenges: (1) multi-scale feature extraction to capture both global shape and fine local geometry; (2) heterogeneous scale normalization to handle meshes with varying sizes and densities;(3) surface-guided gating to suppress internal structures irrelevant to external aerodynamics;and (4) epistemic uncertainty estimation via Monte Carlo dropout for risk-aware design. Extensive evaluations on three industrial-scale datasets (DrivaerNet, DrivaerNet++, and DrivaerML) show that DragSolver outperforms existing approaches in accuracy and generalization, achieving an average reduction of relative $L_2$ error by 58.7% across real-world datasets. Crucially, DragSolver is the first to achieve reliable, real-time $C_d$ inference on production-level automotive geometries.

Applications · Chemistry, Physics, and Earth Sciences

Louis Serrano, Armand Kassaï Koupaï, Thomas Wang, Pierre ERBACHER, patrick gallinari

Solving time-dependent parametric partial differential equations (PDEs) is challenging for data-driven methods, as these models must adapt to variations in parameters such as coefficients, forcing terms, and initial conditions. State-of-the-art neural surrogates perform adaptation through gradient-based optimization and meta-learning to implicitly encode the variety of dynamics from observations. This often comes with increased inference complexity. Inspired by the in-context learning capabilities of large language models (LLMs), we introduce Zebra, a novel generative auto-regressive transformer designed to solve parametric PDEs without requiring gradient adaptation at inference. By leveraging in-context information during both pre-training and inference, Zebra dynamically adapts to new tasks by conditioning on input sequences that incorporate context example trajectories. As a generative model, Zebra can be used to generate new trajectories and allows quantifying the uncertainty of the predictions. We evaluate Zebra across a variety of challenging PDE scenarios, demonstrating its adaptability, robustness, and superior performance compared to existing approaches.

Applications · Chemistry, Physics, and Earth Sciences

Mingquan Feng, Weixin Liao, Yixin Huang, Yifan Fu, Qifu Zheng, Junchi Yan

Neural operators have emerged as a promising approach for solving high-dimensional partial differential equations (PDEs). However, existing neural operators often have difficulty in dealing with constrained PDEs, where the solution must satisfy additional equality or inequality constraints beyond the governing equations. To close this gap, we propose a novel neural operator, Hyper Extended Adaptive PDHG (HEAP) for constrained high-dim PDEs, where the learned operator evolves in the parameter space of PDEs. We first show that the evolution operator learning can be formulated as a quadratic programming (QP) problem, then unroll the adaptive primal-dual hybrid gradient (APDHG) algorithm as the QP-solver into the neural operator architecture. This allows us to improve efficiency while retaining theoretical guarantees of the constrained optimization. Empirical results on a variety of high-dim PDEs show that HEAP outperforms the state-of-the-art neural operator model.

Applications · Chemistry, Physics, and Earth Sciences

Ruocheng Wang, Zhuo Xia, Ge Yan, Junchi Yan

Differential equations are essential and popular in science and engineering. Learning-based methods including neural operators, have emerged as a promising paradigm. We explore its quantum counterpart, and propose QuanONet -- a quantum neural operator which has not been well studied in literature compared with their counterparts in other machine learning areas. We design a novel architecture as a hardware-efficient ansatz, in the era of noisy intermediate-scale quantum (NISQ). Its circuit is pure quantum. By lying its ground on the operator approximation theorem for its quantum counterpart, QuanONet in theory can fit various differential equation operators. We also propose its modified version TF-QuanONet with ability to adaptively fit the dominant frequency of the problem. The real-device empirical results on problems including anti-derivative operators, Diffusion-reaction Systems demonstrate that QuanONet outperforms peer quantum methods when their model sizes are set akin to QuanONet.

Applications · Chemistry, Physics, and Earth Sciences

Seungbeom Lee, Munsun Jo, Jungseul Ok, Dongwoo Kim

Deep learning-based Structure-based drug design aims to generate ligand molecules with desirable properties for protein targets. While existing models have demonstrated competitive performance in generating ligand molecules, they primarily focus on learning the chemical distribution of training datasets, often lacking effective steerability to ensure the desired chemical quality of generated molecules. To address this issue, we propose a multi-reward optimization framework that fine-tunes generative models for attributes, such as binding affinity, validity, and drug-likeness, together. Specifically, we derive direct preference optimization for a Bayesian flow network, used as a backbone for molecule generation, and integrate a reward normalization scheme to adopt multiple objectives. Experimental results show that our method generates more realistic ligands than baseline models while achieving higher binding affinity, expanding the Pareto front empirically observed in previous studies.